expand the expression to a polynomial in standard form: (2x + 1)(2x + 3)(3x - 2)

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Accepted Answer

# Explanation:
## Step1: Multiply first two binomials
First, multiply $(2x + 1)$ and $(2x + 3)$ using the distributive property (FOIL method):
$$
\begin{align*}
(2x + 1)(2x + 3)&=2x\times2x + 2x\times3 + 1\times2x + 1\times3\
&=4x^2 + 6x + 2x + 3\
&=4x^2 + 8x + 3
\end{align*}
$$
## Step2: Multiply the result by the third binomial
Now, multiply $(4x^2 + 8x + 3)$ with $(3x - 2)$ using the distributive property:
$$
\begin{align*}
&(4x^2 + 8x + 3)(3x - 2)\
=&4x^2\times3x + 4x^2\times(-2) + 8x\times3x + 8x\times(-2) + 3\times3x + 3\times(-2)\
=&12x^3 - 8x^2 + 24x^2 - 16x + 9x - 6
\end{align*}
$$
## Step3: Combine like terms
Combine the like terms ($-8x^2 + 24x^2$ and $-16x + 9x$):
$$
\begin{align*}
&12x^3 + (-8x^2 + 24x^2) + (-16x + 9x) - 6\
=&12x^3 + 16x^2 - 7x - 6
\end{align*}
$$
# Answer:
$12x^3 + 16x^2 - 7x - 6$

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QUESTION IMAGE

Question

Explanation:

Step1: Multiply first two binomials

Step2: Multiply the result by the third binomial

Step3: Combine like terms

Answer: